Question

\[x^2 +\sqrt{xy}=xy^5\] compute y'

pls show all steps involved

Answer 1

steps are as if
\[y=f(x), y'=f'(x)\] , chain rule, product rule, etc
\[x^2 +\sqrt{xy}=xy^5\]
\[2x+\frac{xy'+y}{2\sqrt{xy}}=y^5+5xy^4u'\] then algebra to solve for y'